Announcements• Read pages 113-135 of Chapter 5• Discussion Sections: Create Equipment/animal list with Amounts and Vendors (Petco; Biological Carolina Supply; Nature; etc)• Local Pet store run: Monday, March 9th3pm (1-2 persons/group; Sign up with May)• Good Job on EXAMS!• Marked Grade on Exams does not yet include the +7 points (but your grade in my excel spreadsheet does 1Exams• Mean = 72 (pre+7); 79 (corrected,+7)• Median = 75 (pre+7); 82 (corrected, +7)• Stdev = 14.52Today’s Lecture Outline• Adaptive Foraging• Optimal Foraging• Frequency-Dependent Selection & Foraging• Risk Aversion & Foraging3Foraging--Adaptively• Optimal Foraging Theory• Application of Optimality Theory• Pioneered by Robert MacArthur & Eric Pianka (UT) in 1966• IF NS can shape bird wings, why not the foraging BEHAVIOR.• Proposed an OPTIMAL ANALYSIS of diet choice for predators that encounter their prey sequentially.4Crow Foraging Behavior• Crows living in the Northwest often eat on mollusks (snails).• They can’t open them with their beak, so instead they drop fly up to a certain height and drop them.• An Animal Behaviorist noticed that Crows seemed to have a similar foraging behavior (Size of Whelk; Height of Drop)5Crow Whelk Foraging Pattern(Reto Zach)• Crows Picked up only LARGE whelks• Flew up to 5 m to drop them• Would repeat this process (Several flights) until the whelk broke• Reto wanted to know if this behavior was “optimal”• = Maximize whelk flesh available for consumption per unit of foraging time6Crow Optimal Foraging Predictions• Large whelks should be more likely than small ones to shatter at 5m• Drop heights LESS than 5m should yield fewer cracked whelk shells• Drop heigths HIGHER than 5m shouldn’t improve the breakage efficiency• Probability that a whelk will break should be independent of the number of times it has already been dropped.7How Did He Test this?• He built a 15m pole on a rocky beach with a moveable platform (whelk diving board)• He tested whelks of small, medium and large size (pushing them off the platform)• Tested them at different heights• And the results….89Then calculated the Energy Intake per Effort• Calculated avg number of calories required to open a large whelk (0.5Kcal)• The Amount of energy available in a large whelk (2.0 Kcal)• Net Gain = 1.5 Kcal• Compare that to Med-Sized whelks (which require more drops) Net LOSS (0.3Kcal)• And for Small Whelks?10Black-capped Chickadee(e.g. from Giraldeau, 2004)• small NA territorial passerine that feeds on insects to feed itself and nestlings in spring• If chickadees forage proportionately• Then they’ll feed more on common prey= small, commonLess nutritiousprey= Large, rareJuicy prey• Could they do better by being more selective?11Optimal Foraging Reasoning• Could Chickadees nourish young (& itself) more effectively by being choosy?• If so, then NS should favor choosy individuals over non-choosy ones.• So how do we predict the specific degree of choosiness that maximizes a chickadees fitness?12Optimality Models• If we can measure the fitness costs and benefits associated with alternative behaviors, then we can determine which strategy/trait confers the greatest net benefit.• What Behavior is Optimal? W, X, Y or Zor behaviors13Optimal Foraging: Building the Model• Step 1: make explicit ALTERNATIVE Courses of action that we can analyze:– (a) Given an encounter with prey item 2, should the predator eat prey 2, OR– (b) Ignore prey 2 and continue searching?Prey 2 =Prey 1 =• Strategy Should be determined by The Cost & Benefit of Eating Less Profitable Prey verses searching & finding the More Profitable Prey14Hypothesis:• The FUNCTION of prey choice is to MAXIMIZE the RATE OF PREY HARVESTING• Prey Choice maximizes rate of Energy Intake = Energy / Time• E/T = Currency of Fitness or Adaptive Function***Use this Currency to COMPARE the adaptive value between Alternative Courses of ACTION(e.g. Being Choosy or Not Being Choosy)15Currencies & ConstraintsWe have the following:• Decision Rules: [adopt diet that max E/T]• The Currency ( E/T )• Main Constraints[ search time, handling time, encounter rate of different prey items ]• So we can now formulate the predictions16Testing the model:Step 1 Calculate the Currency Curves• Formulate Predictions:• Two Possible Alternative Strategies:– Take ALL PREY encountered (= Generalist, Non-choosy)– ALWAYS attack the MOST Profitable (E/H) prey (Specialist, Choosy)• Compare Value of these 2 approaches:• Need to Calculate their Respective Adaptive Value using the Currency of Fitness.17Our Generalist Currency Equation• E/ T = S(λ1E1 + λ2E2)------------------------------------S + S(λ1H1 + λ2H2)• Where S = search time• E1= energy from consuming prey 1 (BIGGER prey)• E2= energy from consuming prey 2 (smaller prey)1 = encounter rate of prey 12 = encounter rate of prey 2• H1= Handling time of Prey 1• H2= handling time of Prey 218When to Eat Less Profitable Prey?Gain from eating Prey 2 > Gain from rejection2 andsearching for Prey 1E2/h2 > Sλ1E1S + Sλ1H1(the specialist Currency Equation)where S = search time; λ1 = encounter rate for prey 1Prey 1 =19When to Eat Less Profitable Prey?• E2/h2 > Sλ1E1S + Sλ1H1We can rearrange things to get:1 E1 H2------------ > ---------- — H1λ1E220When to Eat Less Profitable Prey?(or when to be a generalist?)• 1/ λ1 > E1H2 - H1E2•Examples: λ1 = 0.20 and λ1 = 0.02• 1 / λ1 = 5 1/ λ1 = 50When More Profitable prey has a Low Encounter Rate21• 1/ λ1 > E1H2 - H1E2• If the above is true? Are you a Specialist or a Generalist?Know This Equation for exam!Notice---Being a Generalist or a Specialist is Driven ONLY byEncounter Rate of LARGE prey item & is INDEPENDENT of theEncounter rate of the Small prey item!!22Suggests that there is some Critical Encounter rate of More Profitable prey that determines Generalist vs Specialist Strategy• Critical Encounter rate, λC• λ1> λCAbove which stay Specialist• λ1< λCBelow which become Generalist(Stephens and Krebs 1986)23Testing the Model• Experimentation• Great tits could view meal worms of 2 sizes passing on a conveyer belt, λ where each prey is varied.• Once a prey is taken, bird must fly to its perch to eat, could not handle and search at the same time.(Krebs et al., 1977)24A test of the Prey